Approximately two-dimensional harmonic $(p_{1},h_{1})$-$(p_{2},h_{2})$-convex functions and related integral inequalities
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Abstract The aim of this study is to introduce the notion of two-dimensional approximately harmonic $(p_{1},h_{1})$ ( p 1 , h 1 ) -$(p_{2},h_{2})$ ( p 2 , h 2 ) -convex functions. We show that the new class covers many new and known extensions of harmonic convex functions. We formulate several new refinements of Hermite–Hadamard like inequalities involving two-dimensional approximately harmonic $(p_{1},h_{1})$ ( p 1 , h 1 ) -$(p_{2},h_{2})$ ( p 2 , h 2 ) -convex functions. We discuss in detail the special cases that can be deduced from the main results of the paper.
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2020 ◽
Vol 10
(1)
◽
pp. 78-84
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